Question

If the sum of the areas of two circles with radii R₁ and R₂ is equal to the area of a circle of radius R, then ______.

Options

• R₁ + R₂ = R

• `"R"_1^2 + "R"_2^2 = "R"^2`

• R₁ + R₂ < R

• `"R"_1^2 + "R"_2^2 < "R"^2`

Answer 1

If the sum of the areas of two circles with radii R₁ and R₂ is equal to the area of a circle of radius R, then `underlinebb("R"_1^2 + "R"_2^2 = "R"^2)`.

Explanation:

According to the question,

Area of circle = Area of first circle + Area of second circle

∴ `π"R"^2 = π"R"_1^2 + π"R"_2^2`

⇒ `"R"^2 = "R"_1^2 + "R"_2^2`